Questions tagged [discretization]

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4
votes
3answers
131 views

Under what conditions is there a one-to-one mapping between continuous-time and discrete-time signals?

As the sampling theorem dictates that the uniform sampling frequency must be at least twice the maximum frequency present in the bandlimited signal (Nyquist rate), a question arises about the ...
0
votes
1answer
52 views

DFT Signal DFT Length N , FFT

If We sample an Signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequecy of Fs = 8Hz, is it right that the length of the data schoul be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
1
vote
1answer
121 views

First Order Hold discrete-time approximation to first order continuous-time linear system

Consider the following first order linear system described by: $\tau \frac{d}{dt}y(t)=-y(t) + x(t)$. I have seen a discrete time approximation to this system using a "First Order Hold" ...
1
vote
1answer
76 views

Impulse Invariant method for digital filter design

One of the known methods for discretizing analog filters is impulse response invariant. We get the impulse response in time domain, discretize it and then get the Z transform. What I am trying to ...
1
vote
2answers
86 views

Discrete-time sampling of filtered white noise

I am trying to understand how I can relate a discrete-time random process to a continuous-time random process sampled at discrete times. Suppose I have a noise source $N_\tau(t)$ which is derived ...
0
votes
1answer
84 views

Discretize process noise in Kalman filter

Reading P. Andrews et al. I see that it is very common to do the following approximation of the process noise covariance matrix: $$Q_{k} = G_{k-1}QG_{k-1}^{T}\Delta t$$ so that the propagation ...
0
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0answers
31 views

Discretizing my continuous system in Matlab

I was hoping someone could help me with conducting my discretization in MATLAB. I have a linear system with known data: sampling interval $T$, system matrix $\mathbf{A}$, input matrix $\mathbf{B}$, ...
3
votes
1answer
524 views

Frequency prewarping of a bilinear transform (Tustin transform)

sadly I'm not too well aquinted with discretazation methods. At the moment I struggle to reproduce a bilinear transform with frequency prewarping. I have the following transfer function in the s-...
0
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1answer
74 views

Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler ...
0
votes
1answer
81 views

Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
0
votes
1answer
337 views

Forward Euler Discretization

I don't understand why the substitution $s=\frac{z-1}{T}$ allows us to discretize a transfer function from laplace to z-transform through Forward Euler Discretization. Can you explain to me ?
3
votes
3answers
182 views

Frequency warping when integrators are replaced with backward-euler and forward-euler integration

Resonant controllers are used in the power industry. The transfer function is $G_{res}(s) = \frac{K_i*s}{s^2 +2*\omega_c*s+ \omega_o^2}$ The "textbook" discrete implementation is depicted in the ...
4
votes
1answer
77 views

s-Domin or z-Domain - What to Use for Mixed systems

I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be ...
0
votes
1answer
208 views

Discretizing a Controller with the Backward Difference Method

In the book "Modern Control Engineering" by Paraskevopoulos it's proved how to discretize a generic controller in the form: $G(s)=\frac{Y(s)}{U(s)}=\frac{a}{s+a}$ where $a$ is a constant. Done this, ...
1
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2answers
100 views

Matlab - Bode plot of Lag Filter + Integrator

I am rather new to Matlab and I just cant make sense of what I see in the bode plot of the continuous and discrete version of the same function. The bode plot of the continuous function looks as ...
2
votes
3answers
2k views

Reduce the Number of Intensity Levels of a Grayscale Image in MATLAB

I have written a Matlab script to reduce the number of intensity levels of each pixel of a grayscale image from 256 to some power of 2. ...
2
votes
2answers
78 views

Kalman Filter: Why $ Q $ Discrete Is Defined as $\int_0^Te^{\mathbf{A}\tau} Q e^{\mathbf{A}^T \tau} d\tau$?

I would like to ask, why in the transformation to the discretization, $\mathbf{Q}$ is obtained from the expression containing the integral (image attached), what is the theory behind it?